Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

Abstract

In the present work, a new class of finite elements (FEs) for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed. By making use of node-by-node variable plate theory assumptions, the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy, in a global/local sense. As a consequence, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states, and their electro-mechanical coupling present a complex distribution. The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements, because the plate structural theory varies within the finite element itself. In other words, the structural theory of the plate element is a property of the FE node in this present approach, and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes. The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modeling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories. Several numerical investigations, such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load, boundary conditions, and piezoelectric material polarizations, are carried out to validate and demonstrate the accuracy and efficiency of the present plate element, including comparison with various closed-form and FE solutions from the literature. ARTICLE HISTORY

Electro-mechanical analysis of composite and sandwich multilayered structures by shell elements with node-dependent kinematics

“…In this work extension actuation, 31-mode, and shear-actuation, 15-mode, are taken into account, for more details see [41]. For the sake of brevity, the expressions that relate the material coefficients C ij to the Young's moduli E 1 ,E 2 ,E 3 , the shear moduli G 12 ,G 13, G 23 and Poisson ratios v 12 ,v 13 ,v 23 ,v 21 ,v 31 ,v 32 are not given here, they can be found in [53].…”

“…The explicit expression of the stiffness electro-mechanical coupling matrices and the pure electric nucleus with classical FEM method are given in Appendix. In the development of ESL and LW theories, the fundamental nucleus of the stiffness matrix is evaluated at the layer level and then assembled at global structure level, for more details the readers can refer to [41,43]. It must be added that, in this work, an MITC technique is used to overcome the shear locking phenomenon, see [49].…”

“…Therefore, between finite elements, the continuity is ensured by adopting the same expansion order in the nodes at the element interface. The present paper is an extension, for shells, of the electro-mechanical analysis of plates structures developed in [41]. This node-dependent finite element has been used by the authors for the mechanical analysis of plates in [42,43] using classical and Higher-Order-Theories (HOT-type) with Taylor polynomials were used with an Equivalent-Single-Layer (ESL) approach, and the combination of HOT-type and advanced Layer-Wise (LW) theories in the same finite element.…”

A Shear-Mode Piezoelectric Heterostructure for Electric Current Sensing in Electric Power Grids

“…In the past several years, the shear effect of the piezoelectric materials has attracted great attention due to the high piezoelectric constant and electromechanical coupling coefficient [15,16,17,18,19,20,21]. Ren et al [15] presented a shear-mode piezoelectric vibration energy harvesting device with a maximum output power of 4.16 mW.…”

Study on Transient Contact-Impact Characteristics and Driving Capability of Piezoelectric Stack Actuator

“…A series of dynamic models and methods for the impact actuator were also developed. Carrera et al [12,13] used the finite element method to analyze the electro-mechanical properties of multilayered piezoelectric structures based on the classical equivalent singlelayer (ESL) model and advanced layer-wise (LW) model. The solutions of ESL, LW, and mixed ESL/LW models are compared.…”